An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is 16, the cap's height is 2, and the cap's radius is 5. What is the object's volume?

1 Answer
Aug 4, 2018

1097.37 cu. I would review my answer and improve and make corrections, if any. Please do not edit this answer.

Explanation:

From the dimensions of the spherical cap, the semi-angle that it

subtends at the center of its sphere,

α rad =arcsin(45)=0.9273,

The side length

of the square top of the prism is 2 (4 ) = 8.

The entire volume = Volume of the cap + volume of the prism

= (( volume of the cone + volume of the

spherical cap ) - volume of the cone) + volume of the prism

=(43(53)αsinα13π(42)(3))+(16)(82)

=43(53)(0.9273)(45)13(3.1416)(9)(3)

#= 1097.37 cu